144 GROWTH PRINCIPLES AND THEORY 2 



the organism is maintained in a state of high order and it even advances, in 

 ontogenesis and evolution, toward states of higher order and heterogeneity. 



Hence, for a considerable time physicists have been puzzled by the apparent 

 violation of laws of physics in living nature. For "how is it possible to understand 

 life when the whole world is governed by such a law as the second law of thermo- 

 dynamics, which points toward death and annihilation?" (Brillouin, 1949). The 

 answer to be given (BertalanfTy, 1932, 1934; Brillouin, 1949; Schrodinger, 1944) 

 is that an expansion of physics is necessary in order to deal adequately with the 

 phenomena of life. It may well happen "that the discovery of new laws and some 

 new principles in biology could result in a broad redefinition of our laws of 

 physics and chemistry, and produce a complete change of point of view" 

 (Brillouin, 1949). This is essentially what has taken place in recent developments 

 of the theory of "open systems". 



By necessity, conventional physical theory, i.e. the physics of closed systems, 

 is inadequate for dealing with living systems. A true biophysics needs a theory 

 of open systems and steady states, which amounts to an extension and generaliza- 

 tion of conventional theory. For it is easy to see that the theory of open systems 

 is the more general one; it is always possible to come from open to closed systems 

 by equating the transport terms to zero, but not vice versa. 



The concept of "open system" was first introduced in biology by BertalanfTy (1932) 

 who indicated several kinetic principles of open systems (1940b, 1950a). Independently, 

 similar considerations were advanced by Burton (1939). Only later was it noticed that 

 the concept of open system had already been used in thermodynamics by Defay (1929). 

 Thennodynamics of open systems is part of the modern expansion of thermodynamic 

 theory known as Irreversible Thermodynamics, founded and developed by Meixner (1954), 

 Onsager (1931), Prigogine (1947, 1955), De Groot (1951), Haase (1952), and others. 



The following discussion is limited to some properties of open systems which 

 are of interest in connection with biological problems of metabolism and growth; 

 for a more detailed discussion of the theory of open systems from the biological 

 standpoint, cf. BertalanfTy (1953), Bray and White (1954, 1957)- 



[b) Definitions 



Before continuing, a definition of terms is in place. A system is called isolated 

 if it exchanges neither matter nor energy with environment; closed if it exchanges 

 energy but not matter; and open if it exchanges both. Conventional kinetics and 

 thermodynamics are limited to isolated and (to a certain extent) closed systems 

 which do not exchange matter with environment. An isolated system must 

 eventually attain a time-independent state, called equilibrium, where all macro- 

 scopic magnitudes remain constant and all macroscopic processes stop. Non-isolated 

 systems may, certain conditions presupposed, attain a time-independent state 

 where also all macroscopic magnitudes remain constant, but macroscopic processes 

 of import and export continue. This is called a stationary state and, in open 

 systems with import and export of matter, a steady state [Fliessgleichgewicht in 

 German: BertalanfTy, 1942a). Chemical equilibria are based upon reversible 

 reactions. Steady states are irreversible as a whole, and partial reactions taking 

 place may also be irreversible. 



